Jay Gopalakrishnan

NH 8

Tue, Thu: 12:00-13:15

Tue 13:15-14:15 (in NH 309)
or by appointment (email: gjay@pdx.edu).

Every mathematical scientist and engineer needs to work with
matrices and vectors analytically and numerically. The
course aims to teach often needed tools for computations with
linear operators.

This is the first part of a three-part year-long advanced sequence on
techniques for scientific computation.
The three parts are loosely organized as follows:

*Plan for this quarter (Part 1) : *

- Part 1: Numerical linear algebra
- Part 2: Finite elements and finite differences
- Part 3: Nonlinear techniques

- SVD
- Iterative techniques

Orthogonal and oblique projections.
Singular value and other decompositions.
Solution techniques for dense systems.

Conjugate Gradient algorithm,
Arnoldi, Lanczos, and other Krylov space iterations,
gmres,
multigrid iteration,
basic preconditioning techniques.

(Eigenvalue algorithms moved to another term)

*Numerical Linear Algebra*, by Lloyd N. Trefethen and David Bau III.*Matrix Computations*, by Gene H. Golub and Charles F. van Loan*Iterative Methods for Sparse Linear Systems*by Y. Saad

You are not required to buy any of these.

Grades will be assigned based on take-home projects. Projects
can be computational or theoretical, and can be tailored to
student background and preferences.